The National Theatre will stage a musical Tori Amos has written based on The Light Princess, a fairytale by George MacDonald. Photograph: Astrid Stawiarz/Getty Images

A musical by the singer-songwriter Tori Amos, a new drama by Mike Leigh and Simon Russell Beale as Stalin are all part of a defiantly ambitious programme for the coming year at the National Theatre, with artistic director Nicholas Hytner declaring that the only response to expected funding cuts was to be "bullish in our programming".

Russell Beale's Stalin will be seen in a debut stage play by John Hodge, who wrote screenplays for Danny Boyle's early films, including Shallow Grave, A Life Less Ordinary and Trainspotting.

His script – about an imagined meeting between the author Mikhail Bulgakov and Stalin – was sent in to the National on spec; it is mere coincidence that his old collaborator Boyle's vision of Frankenstein opens at the theatre next month. Alex Jennings will play Bulgakov and Hytner directs. Hytner called Hodge "a wonderful dramatist even though he comes from the world of film and TV".

The Amos musical is loosely based on The Light Princess, a fairytale by the 19th-century Scottish writer George MacDonald. The book and additional lyrics are by Samuel Adamson, and Marianne Elliott will direct.

The theatre will also stage a documentary musical, directed by Rufus Norris, called London Road, with book and lyrics by Alecky Blythe.

The theatre's Christmas show will be a departure. Instead of a children's book adaptation, such as its hugely successful War Horse, it will present Shakespeare as a show for all the family, with Dominic Cooke, director of the Royal Court Theatre, making his debut at the National with A Comedy of Errors.

As is customary, the title and subject of Leigh's new play, which opens in September, are unknown to all but the playwright-director and the cast, which includes Lesley Manville. "I have absolutely no idea what it's about," said Hytner. "I expect I'll find out at the first preview."

James Corden will take the lead in a new version by Richard Bean of Carlo Goldoni's A Servant With Two Masters. Renamed One Man, Two Guvnors, it will be set in 1960s Brighton rather than 18th-century Venice. Hytner will direct. Corden made his name in Alan Bennett's The History Boys at the theatre. Hytner said: "That was an extraordinary group of young actors. James was then and has become a really accomplished comic actor with a really vivid personality". The production, he said, would "subvert the concrete elegance of this building".

Hytner announced a new initiative to help two regional theatres with fundraising – an increasing source of income in the arts as public money ebbs. Its first partner will be the Bristol Old Vic, now run by former associate director of the National Tom Morris. "The theatre does amazing work," said Hytner, "but it is doing relatively badly at attracting individual giving. We will work with them for a couple of years at board and executive level."

Hytner said box office receipts had been unaffected by the economic climate, with 100% of tickets sold over the past five weeks. The Travelex £10 tickets for seats in the Olivier are to be raised to £12 after eight years, a rise just under inflation. "It is cheaper than a seat at a West End cinema," said Hytner.